It has long been believed that the standard design-based approach to sample survey inference and the prediction-based approach used by Royall and his co-authors are so radically different as to be incompatible. However it is now possible to combine them in a useful way; the design-based approach being particularly suitable for large samples and the prediction-based for small samples (and small domains within large ones). The variances of the resulting estimators can be considered using either approach separately or both together. All the relevant variance formulae and estimators are simple, easily understood and straightforwardly related; and there is a further spin-off in the avoidance of unacceptable sample weights.